Nano-Lens And Micro-Lens Simulations

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Finite-Difference Time-Domain Simulation Design

Nano-Lens And Micro-Lens Simulations (FDTD)



When optical lens size is compatible with the working wavelength, the traditional lens analysis tools such as ray-tracing method will lose their accuracy. The FDTD method can be used to advantage in the nano-lens simulation. OptiFDTD software also provides tools so that beam focus size, focus distance, and far-field transform can be obtained directly. The following two samples show nano-lens simulations.




SMF28 fiber lens simulation



Layout Introduction



When fiber is tapered and polished in the termination as shown in Figure 1, a fiber lens can be created. The lens size can be exactly fiber’s core size or smaller than the core. In fact OptiFDTD can scan the lens size so that focus beam size and focus distance can be optimized.




SMF28 fiber lens R=6 µm


SMF28 fiber lens R=2.4µm


Figure 1: SMF28 fiber lens (a) R=6 µm; (b) R=2.4µm




Related layout can be found in OptiFDTD sample folder with project name “Sample22_VBscript_2D_Lens.FDT”



Simulation results



After the simulation, the field pattern and the Poynting vector can be plotted for each lens size (see figure 2), based on the field pattern, the beam size and the focus distance can be measured by the slice viewer (see figure 3)




FDTD -  Poynting vector for Fiber lens

Figure 2: Poynting vector for Fiber lens




FDTD -  Beam size measurement in OptiFDTD

Figure 3: Beam size measurement in OptiFDTD




Nano Lens Array



In this 3D sample, we discuss a micro-lens array, the lens dimension is marked in Figure 1, and Figure 2 is xy plane refractive index distribution.




FDTD -  Micro-lens array size

Figure 1: Lens size




FDTD -  Top view if the lens Array

Figure 2: Top view of the lens Array




Simulation Parameters

  • • Mesh size : 0.02um*0.02um*0.02um
  • • Run for 1248 time step +
  • • 10 additional cycle to get the steady state field
  • • Calculate steady state field for Ey and Hx (Discretized Fourier transform)
  • • x-y boundary use the upper-lower symmetric boundary condition. Z-direction user the APML as the boundary condition




FDTD -  Simulation parameters

Figure 3: Simulation parameters




Simulation results



As shown in figure 4, in the simulation we can observe the time domain response in each slice in three orientations ( xy plane, yz plane, xz plane)




FDTD -   time domain response in xz plane

Figure 4: Time domain response in xz plane




Steady state response can be observed in analyzer as shown figure 5. Beam size and focus distance can be measured in OptiFDTD as shown in figure 6




FDTD -  Field pattern in xy plane

Figure 5: Field pattern in xy plane




FDTD -   Field pattern in xz plane

Figure 6: Field pattern in xz plane




The calculation shows that each lens focuses at z=1.26, focus distance 1.26-0.8=0.46um



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